Square roots of perfect squares — Vedic maths trick

The trick

Vilokanam — “by observation”

1. Last digit → the root ends in one of two digits: 1↔9, 4↔2/8, 9↔3/7, 6↔4/6, 5→5, 0→0.
2. Remove the last two digits; the biggest square not more than what is left gives the tens digit.
3. Pick the ending: compare the number with (tens × 10 + 5)² — bigger means the bigger ending.

Use it for: Perfect squares up to 4 digits (roots 11–99).

Worked example: √5184 = 72

✏️ Practice

Work it out in your head or on paper, then tap your answer — or type it and press Check. Stuck? Press “Show me how”.

🏁 Trick 9 test

20 sums. Check each answer, then go to the next one. Get 16 or more right to pass.

🏅 Sign in with Google to earn the 🌱 Root Finder badge when you pass — and a certificate when you finish all 10 tricks of Part 1 · Core tricks. You can still take the test without signing in.

🖨️ Square Root Worksheet

• Worksheet set 1 (PDF)
• Worksheet set 2 (PDF)
• Worksheet set 3 (PDF)